Finite element methods for viscoelastic multiphase flows using a conservative level set approach

Doherty, William 2024. Finite element methods for viscoelastic multiphase flows using a conservative level set approach. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This thesis is concerned with the stable and accurate representation of viscoelastic multiphase flows in both planar and axisymmetric coordinate representations. A computational approach is taken, where the governing equations for viscoelastic fluid flow and multiphase interface representation are derived and then discretised using the finite element method. The numerical scheme is then implemented on classical and contemporary research problems. The numerical approximation of viscoelastic fluids exhibit large variations in stress near boundary layers and fluid interfaces, increasingly more so the more polymer present in the fluid. This makes direct numerical simulations difficult as they become rapidly plagued with stability issues. In this work a number of formulations for stabilising the numerical scheme are explored. In particular, the seminal work of Fattal and Kupferman (2004) who introduced a log-conformation formulation for the constitutive equation is expanded here for general rheological models under an axisymmetric assumption. The conservative level set method of Olsson and Kreiss (2005) is the chosen interface representation algorithm for this thesis. It is implemented for the first time on certain viscoelastic fluid flow problems contained presented here. One of the main developments to the method is the novel reformulation of the diffused interface approach of Xie et al. (2016) for the stable calculation of the normal to the interface. Benchmarks for single and multiphase viscoelastic flow are considered to validate the numerical scheme presented. Additionally much attention is paid to the representation of viscoelastic phenomena found for bubbles and drops. The cases considered are contemporary research areas with less coverage in the literature when compared with their Newtonian counterparts. For example, multiple difficult to predict phenomena for a rising gas bubble in a viscoelastic fluid are found by the numerical scheme and agree well with experimental data. This is investigated with respect to polymeric stress distributions and velocity fields, only made possible through the use of a high resolution numerical scheme. This same scheme is then applied to the completely novel case of a iv viscoelastic droplet impacting a deep pool, where new insights into the fluid mechanics of the problem are drawn.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Engineering
Uncontrolled Keywords:	1) Viscoelastic flow 2). Multiphase flow 3). Finite element methods 4). Non Newtonian fluids 5). Conservative level set method 6). Rising bubble
Date of First Compliant Deposit:	8 November 2024
Last Modified:	08 Nov 2024 16:35
URI:	https://orca.cardiff.ac.uk/id/eprint/173787

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